Question

tools reference point at (1, $10) reference point at (3, $6) reference point at (4, $4) legend demand point 1 at (1,10) point 2 at (3, 6) point 3 at (4, 4) demand for dogs playing poker what price should you charge if your goal is to maximize your revenues from tickets sold? instructions: enter your answer as a whole number. $ per visit.

Explanation:

Step1: Recall revenue - quantity relationship

Revenue $R = P\times Q$, where $P$ is price and $Q$ is quantity.

Step2: Calculate revenue at different points

At point $(1,10)$: $R_1=1\times10 = 10$.
At point $(3,6)$: $R_2=3\times6=18$.
At point $(4,4)$: $R_3=4\times4 = 16$.
We can also note that for a linear - demand curve, revenue is maximized when the price - elasticity of demand is unit - elastic. On a linear demand curve, unit - elasticity occurs at the mid - point of the demand curve. The general form of a linear demand curve is $P=a - bQ$. The revenue function is $R = P\times Q=(a - bQ)Q=aQ - bQ^{2}$. To find the maximum of the revenue function, we take the first - derivative with respect to $Q$ and set it equal to zero. $\frac{dR}{dQ}=a - 2bQ = 0$, which gives $Q=\frac{a}{2b}$. And $P=\frac{a}{2}$.
Looking at the demand curve, we can calculate revenue for integer values of $Q$ and $P$ along the curve.
We can see that the revenue is maximized when $P = 6$ and $Q = 3$ with a revenue of $18$.

Answer:

6